Question

In: Finance

Your sister is the one lucky winner of the Ohio Lottery and is looking to you,...

Your sister is the one lucky winner of the Ohio Lottery and is looking to you, as a Finance Major, to help out with some advice. Assuming market interest rates are at 4.00%, on a present value basis how would you consult with her about the choice to

- take an annuity of $2,200 per month for 25 years, or

- take an annuity of $2,400 per month for 20 years ?

- how much is she better off by choosing the one you recommend, remembering that more is better!

Solutions

Expert Solution

The present value of 1st annuity will be as follows:

Present value = Monthly payment x [ (1 – 1 / (1 + r)n) / r ]

r is computed as follows:

= 4% / 12 (Since the payments are on monthly basis, hence divided by 12)

= 0.333333%

n is computed as follows:

= 25 year x 12 months (Since the payments are on monthly basis, hence multiplied by 12)

= 300

So, the amount is computed as follows:

= $ 2,200 x [ (1 - 1 / (1 + 0.0033333)300 ) / 0.0033333 ]

= $ 2,200 x 189.4524909

= $ 416,795

The present value of 2nd annuity will be as follows:

Present value = Monthly payment x [ (1 – 1 / (1 + r)n) / r ]

r is computed as follows:

= 4% / 12 (Since the payments are on monthly basis, hence divided by 12)

= 0.333333%

n is computed as follows:

= 20 year x 12 months (Since the payments are on monthly basis, hence multiplied by 12)

= 240

So, the amount is computed as follows:

= $ 2,400 x [ (1 - 1 / (1 + 0.0033333)240 ) / 0.0033333 ]

= $ 2,400 x 165.021864

= $ 396,052

So, the first annuity shall be preferred and the same is greater than the 2nd annuity by the amount of:

= $ 416,795 - $ 396,052

= $ 20,743

Feel free to ask in case of any query relating to this question


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